Writing a congruence in order
Two triangles are cut from cloth. Which corner of one lands on which corner of the other?
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The rule
In ΔABC ≅ ΔXYZ, the letters match in order. Δ means triangle. ≅ means is congruent to. A matches X, B matches Y, and C matches Z. Matching sides are equal. Matching angles are equal.
Take P matching U, Q matching V and R matching T. Then ΔPQR ≅ ΔUVT is right. Five more ways are also right.
| First triangle | Second triangle |
|---|---|
| ΔPQR | ΔUVT |
| ΔPRQ | ΔUTV |
| ΔQPR | ΔVUT |
| ΔQRP | ΔVTU |
| ΔRPQ | ΔTUV |
| ΔRQP | ΔTVU |
Each row changes the order of both names in the same way. So each row says the same thing.
Watch out!
"ΔPQR ≅ ΔUVT and ΔPQR ≅ ΔUTV say the same thing." Not so. In the first, Q matches V. In the second, Q matches T.